Q5: Car 1 brakes to a stop on a dry road. Car 2 does the same thing, at the same speed, on a road where it has been raining.

The x-intercepts from the graph are -3.646 and 1.646 with the parabolic curve facing upwards

Quadratic functions are functions that has a leading coefficient of 2.

According to the question, we are to graph the quadratic function f(x) = x^2 + 2x - 6. The curve will be parabolic in nature and facing upwards since it is a quadratic function.

The x-intercepts from the graph are -3.646 and 1.646 as shown in the attached graph.

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Answer:

4 !!!

Step-by-step explanation:

We integrate the remaining integral: ∫(5x - (1/2)x^2) dx = (5/2)x^2 - (1/6)x^3 + C The final result is: ∫x(5 - x) dx = x(5x - (1/2)x^2) - ((5/2)x^2 - (1/6)x^3) + C

To integrate x^5 - x dx by parts, we need to choose u and dv. Let's choose u = x^5 and dv = (5 - x) dx. Then du/dx = 5x^4 and v = ∫(5 - x) dx = 5x - (1/2)x^2 + C.

Now, using the formula for integration by parts, we have:

∫x^5 - x dx = u*v - ∫v*du/dx dx
= x^5(5x - (1/2)x^2) - ∫(5x - (1/2)x^2)*5x^4 dx
= 5x^6 - (1/2)x^7 - (5/6)x^6 + (1/20)x^5 + C
= (9/20)x^5 - (7/6)x^6 + 5x^6 + C

Therefore, the antiderivative of x^5 - x dx using integration by parts with dv = 5 - x dx is (9/20)x^5 - (7/6)x^6 + 5x^6 + C.

To consider the following integral: ∫x(5 - x) dx, we will integrate by parts, letting dv = (5 - x) dx.

To integrate by parts, we use the formula ∫u dv = uv - ∫v du. In this case, we have:

u = x, so du = dx
dv = (5 - x) dx, so v = ∫(5 - x) dx = 5x - (1/2)x^2

Now, we can plug these values into the formula:

∫x(5 - x) dx = x(5x - (1/2)x^2) - ∫(5x - (1/2)x^2) dx

To finish, we integrate the remaining integral:

∫(5x - (1/2)x^2) dx = (5/2)x^2 - (1/6)x^3 + C

So, the final result is:

∫x(5 - x) dx = x(5x - (1/2)x^2) - ((5/2)x^2 - (1/6)x^3) + C

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The radius of the circle, to 1 decimal place, is approximately 5.33 cm.

The confusion earlier.

Let's calculate the radius of the circle with an area of 89 cm².

The formula for the area of a circle is:

Area = π × r²

Given the area is 89 cm², we can rearrange the formula to solve for the radius (r):

r = √(Area / π)

Substituting the given area value:

r = √(89 / π)

To calculate the radius to 1 decimal place, we need to approximate the value of π.

Taking π as approximately 3.14, we can compute:

r ≈ √(89 / 3.14)

r ≈ √(28.344)

r ≈ 5.33 cm (rounded to 1 decimal place)

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An exponential function is a function in the form y = a^x, where a is a positive constant called the base.

The inverse of the exponential function with base a is called the logarithmic function with base a, denoted as y = loga(x).

An exponential function is represented by the equation

y = a^x,

where a is the base, and the inverse of the exponential function is the logarithmic function with base a, denoted as

y = loga(x).

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9514 1404 393

Answer:

  3. 8; 29; 11; 12

  4. B. 11, 5, 13

  5. D. sides are 1; hypotenuse is √2

Step-by-step explanation:

3. Each of these can be figured from the Pythagorean theorem. The right-most blank is presumed to be the hypotenuse, so for all but the second blank the missing number is the root of the difference of the squares. Interestingly, you can compute this in your head by using the factoring of the difference of squares:

  a = √(c^2 -b^2) . . . . . . where c is the hypotenuse

  a = √((c +b)(c -b)) . . . . difference of squares is factored

For the first, this is b = √((10+6)(10 -6)) = √(16·4) = 4·2 = 8

For the third, this is a = √((61+60)(61-60)) = √121 = 11

For the fourth, this is b = √((13+5)(13-5)) = √(18·8) = √(9·2·2·4) = 3·2·2 = 12

For the second blank, we can do it the usual way:

  c = √(20² +21²) = √(400 +441) = √841 = 29

The blanks are filled with 8, 29, 11, 12.

Note: You may notice that (6, 8, 10) is double the triple (3, 4, 5). The triple (5, 12, 13) comes into play in the next problem.

__

4. The first few Pythagorean triples are (3, 4, 5), (5, 12, 13), (7, 24, 25). It can be useful to remember these.

By comparing these to the first three choices, you can see that choice B lists three numbers that cannot be a right triangle. (If the shortest and longest sides are 5 and 13, then the other side must be 12 if it is a right triangle.)

__

5. Darnell's finding that 1² +1² = (√2)² means that a triangle with sides in the ratio 1 : 1 : √2 is a right triangle. This description matches choice D.

Note: It can be useful to remember that sides 1 : 1 : √2 make an isosceles right triangle. It means the diagonal of a square is √2 times the side length, for example.

Hence, in response to the provided question, we can say that As a result,  arithmetic progression the usual difference is d = -30.

The difference between subsequent terms in a string will never vary, and this is referred like an arithmetic progression. The sequences 5, 7, 9, 11, 13, through 15 are examples of arithmetic progressions with a tolerance of 2. Arithmetic progression (A.P.) is a progression that has a set tolerance between any 2 consecutive values. Numerical progression may fall into one of two main types: finite-length arithmetic series A finite geometry progression is a series with just a fixed number of terms. The series' terms can be used to calculate the early, late, leniency, and number of term.

A) The sequence is, indeed, arithmetic.

We can find the common difference by subtracting any two consecutive terms:

109 - 9 = 100

209 - 109 = 100

309 - 209 = 100

As a result, the typical difference is d = 100.

A) The sequence is, indeed, arithmetic.

We can find the common difference by subtracting any two consecutive terms:

-32 - (-2) = -30 \s-62 - (-32) = -30 \s-92 - (-62) = -30

As a result, the usual difference is d = -30.

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Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

Answer:

Using the formulas

A=6a2

V=a3

Solving for V

V=6A3/2

36=6·543/2

36≈27

Answer:

Step-by-step explanation:

Answer:

V = 3078.76 in³

Step-by-step explanation:

To find the volume of a cylinder, use this formula:

V = πr²h

Plug in the values you know.

V = π(7)²(20)

First let's evaluate the exponent.

7² = 49

V = π(49)(20)

Now let's multiply.

49 • π = 153.938

153.938 • 20 ≈ 3078.76

V = 3078.76 in³

This is your answer.

Hope this helps!

Answer:

2.26666667

Step-by-step explanation:

Stay Frosty

Answer:

28/15

Step-by-step explanation:

Answer:

1,027 milliliters

Step-by-step explanation:

1 liter is 1,000 milliliters

2 centiliters is 20 milliliters

7 milliliters stays the same

Adding up the new numbers gives you

1,000+20+7

Answer: -2

Step-by-step explanation:

Answer:

You have to write the number-line out man. However, the answer is -2

Step-by-step explanation:

When solving problems like these, knowledge or integers and whole numbers are important. First, find the absolute values of both numbers.

Absolute value of -6: 6

Absolute value of 4: 4

Subtract the values: 6 - 4 = (Positive 2)

THEN, look at the number with the Greater Absolute value. In this case, it is -6. Because -6 has the greater absolute value, your answer should be the connotation of that number. IN THIS CASE, the number with the greater absolute value, -6, has a negative sign. Therefore, your answer should be negative. Your answer is -2.

My attempt at a number line:

----------------->

_|_________|______________

-6  -5  -4 - 3  -2  -1  0  1  2  3  4

Answer: They are related by the AAS postulate and they can be proven congruent.

Step-by-step explanation: You can see that one of the lines on each of the triangle has that little tick which means those lines are congruent. You can also see that for two of the angles one of them has one arc and the other has two arcs for BOTH triangles which makes those two angles congruent. Two angles and one side congruent makes the triangles congruent by the AAS postulate.

I hope I helped! :)

Answer:

red ball=3

yellow ball=6

green ball=9

total=18

probably of getting both red and yellow=3/18×6/18

1/18

the probability is 1/18

the Laplace transform of the given function f(t) is:

\(F(s) = s^{-2}[(1 - s)e^{-2s} - (1 + s)e^{-3s}]\)

To find the Laplace change of the given capability, we really want to utilize the properties of the Laplace change and compose the capability in a reasonable structure.

First, let's write the function in a different way by expanding the terms and using the definition of the unit step function u(t):

\(f(t) = (t - 3)u2(t) - (t - 2)u3(t)\\= tu2(t) - 3u2(t) - tu3(t) + 2u3(t)\\= tu2(t) - tu3(t) - 3u2(t) + 2u3(t)\)

Now, we can take the Laplace transform of each term separately using the linearity property of the Laplace transform:

\(L{tu2(t)} = -\frac{d}{ds}L{u2(t)} = -\frac{d}{ds}\frac{1}{s^2} = \frac{2}{s^3},L{tu3(t)} = -\frac{d}{ds}L{u3(t)} = -\frac{d}{ds}\frac{1}{s^3} = \frac{3}{s^4},L{u2(t)} = \frac{1}{s^2},L{u3(t)} = \frac{1}{s^3}.\)

Using these results, we can write the Laplace transform of f(t) as:

\(F(s) = L{f(t)} = L{tu2(t)} - L{tu3(t)} - 3L{u2(t)} + 2L{u3(t)}\\= \frac{2}{s^3} - \frac{3}{s^4} - 3\frac{1}{s^2} + 2\frac{1}{s^3}\\= \frac{2 - 2s e^{-2s} - 3e^{-3s} + 3s e^{-3s}}{s^3}\\\)

Simplifying the expression, we get:

\(F(s) = \frac{s e^{-3s} - se^{-2s} - 1 + e^{-3s}}{s^3}\\= \frac{s e^{-3s} - se^{-2s}}{s^3} - \frac{1 - e^{-3s}}{s^3}\\= s^{-2}[(1 - s)e^{-2s} - (1 + s)e^{-3s}]\)

Therefore, the Laplace transform of the given function f(t) is:

\(F(s) = s^{-2}[(1 - s)e^{-2s} - (1 + s)e^{-3s}]\)

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Answer:

The height of the tree to the nearest foot is 75.

Step-by-step explanation:

The height is opposite the angle of elevation, and the 45 ft distance to the tree is adjacent to it.

tangent = opposite/adjacent

\(\frac{tan(59)}{1} = \frac{h}{45}\)

h = tan(59) * 45

h ≈ 74.89

To the nearest foot, 74.89 is 75 ft.

Answer:

216 cubic inches

Step-by-step explanation:

(9)(3)(3)=81

(3)(3)(9)=81

(3)(3)(6)=54

81+81+54=216

So, it's 216 cubic inches in volume.

Answer:

12.5 miles per hour

Step-by-step explanation:

The speed is the distance divided by time.

3.75 miles/0.3 hours= 12.5 miles per hour

Answer:

12.5 miles per hour

Step-by-step explanation:

To answer this question you have to make sure that the hours (denominator) equals to 1. To do this, divide 3.75 by 0.3, thus making the 0.3 hours into 1 hour. This results in 12.5 miles per hour, the correct answer. Hope this helped!

Hello, the solution is in this photo.

The correct answer is 300

Answer:

300cm^2

Step-by-step explanation:

Replace pie by 3. 3(10)^2 which equals to 300cm^2. 10 is radius.

4.01% of the original sales will require replacement after 1 year.

Z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

\(z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard \ deviation\)

Given that mean = 3.1, standard deviation = 1.2, hence:

For x < 1:

z = (1 - 3.1)/1.2 = -1.75

From the normal distribution table:

P(z <  -1.75) = 0.0401 = 4.01%

4.01% of the original sales will require replacement after 1 year.

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Answer:

735

Step-by-step explanation:

7 * 5 * 21 = 735 outfits

The woman can create 735 outfits.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

To find the total number of outfits that can be created, we need to multiply the number of options for each item.

For each blouse, there are 5 options for a skirt, and 21 options for a pair of shoes.

So, the total number of outfits can be calculated as:

7 blouses x 5 skirts x 21 pairs of shoes = 735

Therefore, the woman can create 735 outfits.

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Answer:

-r + 9

Step-by-step explanation:

Like terms are those with the same variable

Ex. Lets say we have 4a + 4b + 2a.

4a and 2a would be like terms as they share the same variable, the variable being a.

We have 4r - 6r + 9 + r

9 is by itself so we leave it as it is

The like terms would be 4r, -6r and r as they share r for a variable

So we simply combine ( add ) them together

4r + (-6r) + r = - r

We are left with - r + 9

Answer:

usage patterns are a variable used in market segmentation.

Step-by-step explanation:

Usage patterns are a variable used in behavioral segmentation.

Behavioral segmentation is a marketing strategy that divides a market into different segments based on consumer behavior, specifically their patterns of product usage, buying habits, and decision-making processes. This segmentation approach recognizes that customers with similar behavioral characteristics are likely to exhibit similar preferences and respond in a similar manner to marketing initiatives.

Usage patterns, as a variable, help marketers understand and classify customers based on how they interact with a product or service. This can include factors such as the frequency of product usage, the amount of product used, the timing of purchases, brand loyalty, product benefits sought, and other behavioral indicators.

By analyzing usage patterns, marketers can identify distinct segments within their target market and tailor marketing strategies to meet the unique needs and preferences of each segment. This enables companies to develop more targeted marketing campaigns, optimize product offerings, improve customer satisfaction, and drive customer loyalty.

Overall, behavioral segmentation, including the consideration of usage patterns, allows companies to better understand and connect with their customers by aligning their marketing efforts with specific behaviors and motivations.

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Answer:

7/12

Step-by-step explanation:

The equation of the hyperbola for the cross section of the cooling tower is x²/8100 - y²/9506.25 = 1.

We must take into account its characteristics in order to formulate the hyperbola's equation for the cooling tower's cross section.

Since the origin serves as the hyperbola's centre, its coordinates are (0, 0).

The left/right opening of the hyperbola indicates that the primary axis is horizontal.

The cooling tower's smallest diameter is 180 metres, which is the same length as the minor axis.

The primary axis' 195 m length and the diameter at its highest point are matched.

The hyperbola's highest point is 80 metres above the centre.

These characteristics allow us to write the hyperbola's equation in standard form:

(x - h)²/a² - (y - k)²/b² = 1

Where (h, k) represents the center of the hyperbola.

Substituting the given values:

Center: (h, k) = (0, 0)

Minor axis: 2a = 180 m, so a = 90 m

Major axis: 2b = 195 m, so b = 97.5 m

Vertical shift: c = 80 m

Now we can write the equation of the hyperbola:

x²/90² - y²/97.5² = 1

Simplifying, we have:

x²/8100 - y²/9506.25 = 1

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Answer:

Step-by-step explanation:

30-2(7+2)-1

= 30 - 2(9) - 1

= 30 - 18 - 1

= 11

Let,

Perform the operation (1)+(2),

Substitute the value of x=-2/5 in the expression (1).

Thus, the value of x is -2/5 and value of y is -96/25.